1. Field of the Invention
The invention is related to the field of interpretation of data from well logging instruments comprising a plurality of exponentials. More specifically, the invention is related to methods of processing measurements from a pulsed neutron well logging instrument for determining various properties of earth formations penetrated by a wellbore. The processing method enables separating various components of the signals from the instruments to obtain parameters of interest.
2. Background of the Art
Pulsed neutron well logging instruments are known in the art for determining the macroscopic thermal neutron capture cross-section of earth formations penetrated by a wellbore. A typical pulsed neutron well logging instrument is described, for example, in a sales brochure entitled PDK-100, Western Atlas Logging Services, Houston, Tex. (1994). Typical pulsed neutron instruments include a controllable source of high-energy neutrons, and one or more gamma ray radiation detectors positioned at spaced apart locations from the neutron source. The source is periodically activated to emit controlled-duration xe2x80x9cburstsxe2x80x9d of high- energy neutrons into the earth formations surrounding the well borehole. The neutrons interact with atomic nuclei of the materials in the earth formations, losing energy with each interaction until the neutrons reach the thermal energy level (defined as having a most likely energy of about 0.025 electron volts). Depending on the material composition of the earth formations proximal to the instrument, the thermal neutrons can be absorbed, or xe2x80x9ccapturedxe2x80x9d. at various rates by certain types of atomic nuclei in the earth formations. When one of these atomic nuclei captures a thermal neutron it emits a gamma ray, referred to as a xe2x80x9ccapture gamma rayxe2x80x9d.
The rate at which the capture gamma rays are emitted, with respect to the elapsed time after the end of the neutron xe2x80x9cburstxe2x80x9d depends on, among other things, the relative concentration per unit volume in the earth formations of atomic nuclei which have a relatively large tendency to absorb thermal neutrons and emit capture gamma rays in response. This tendency is referred to as the thermal neutron capture xe2x80x9ccross-sectionxe2x80x9d. A common chemical element found in earth formations having high capture cross-section atomic nuclei is chlorine. Chlorine in earth formations is usually present in the form of chloride ion in solution in connate water present in the pore spaces of some of the earth formations. Chlorine has a very high thermal neutron capture cross- section. Thus a measurement of the thermal neutron decay time (or neutron lifetime) of the earth formations in the vicinity of the wellbore can be indicative of amount of saline fluid present in the pore spaces of the earth formation. When combined with values of connate water salinity, fractional volume of pores space (xe2x80x9cporosityxe2x80x9d), and measurements of the fractional content of fine gained particles in the formation (xe2x80x9cformation shalinessxe2x80x9d) it is possible to determine the fractional fluid saturation of useful materials, such as oil or gas, present in the pore spaces of the earth formation.
It has proven difficult to determine the fractional saturation of oil or gas under certain wellbore conditions by processing the capture gamma ray measurements according to methods known in the art for determining the thermal neutron capture cross-section, xcexa3f of the earth formation of interest. Several factors contribute to the difficulty of determining xcexa3f using the methods known in the art. First, the well logging instrument is typically inserted into a wellbore which is filled with liquid. At the time the pulsed neutron instrument is typically used, the wellbore generally has inserted therein a steel liner or casing. The liner or casing is generally held in place by cement filling an annular space between the wellbore wall and the exterior of the liner or casing. As high energy neutrons leave the neutron source in the logging instrument, the liquid in the wellbore has the effect of rapidly moderating (or slowing down) the high energy neutrons to the thermal level because of the high concentration of hydrogen nuclei in the liquid.
In general, the relative numbers (xe2x80x9cpopulationxe2x80x9d) at any particular time after a neutron burst, of thermal neutrons in the wellbore and in the earth formations proximal to the wellbore will depend on the porosity and on the hydrogen nucleus concentration per unit volume within the earth formation. The thermal neutrons present in the wellbore and in the earth formations can be xe2x80x9ccapturedxe2x80x9d or absorbed by nuclei of various chemical elements in the wellbore and formations, at a rate which depends upon the relative concentration and on the thermal neutron capture cross-section of these elements. In wellbores and in earth formations some of the more common elements having high thermal neutron cross-sections include chlorine, hydrogen, iron, silicon, calcium, boron, and sulfur. The thermal neutron decay time or xe2x80x9cneutron lifetimexe2x80x9d, as determined from measurements of capture gamma rays made by the well logging instrument, represents combined effects of the thermal neutron capture cross-section in each of several xe2x80x9cregionsxe2x80x9d(volumes of space surrounding the logging instrument) within the wellbore as well as from the earth formations proximal to the wellbore. These regions generally include the instrument itself, the fluid in the wellbore, the steel casing, the cement, the earth formation radially proximal to the wellbore wall (which may have been infiltrated by fluid from within the wellbore), and the earth formations radially more distal from the wellbore wall (which have minimal infiltration from the fluid in the wellbore).
Determining xcexa3f using data processing methods known in the art can be further complicated if the earth formation does not have a truly homogenous material composition on the scale of measurements made by the well logging instrument. Conditions in the earth formations subject to this difficulty can include earth formations consisting of a layered xe2x80x9csand/shalexe2x80x9d sequence wherein the layers are on the order of 3-4 inches thick, or can include the presence of a fluid transition zone such as a gas/oil or an oil/water contact in the earth formation. Other conditions can include the presence of a radial zone located within approximately 2-8 inches from the wellbore wall having a different fluid than in a radially more distal zone, this being familiar to those skilled in the art as being caused by such processes as xe2x80x9cinvasionxe2x80x9d(the previously described fluid infiltration), and gas or water xe2x80x9cconingxe2x80x9d as well as other processes known in the art.
The capture gamma ray detection rate as measured by the logging instrument will necessarily include fractional contributions from all of the regions in the vicinity of the logging instrument. Each of these regions has an indeterminate fractional contribution to the overall capture gamma ray counting rate as measured by the logging instrument, and can also have an unknown value of capture cross-section
Several processing methods are known in the art for determining the macroscopic thermal neutron capture cross-section of the formation, xcexa3f, from the measured capture gamma ray counting rates with respect to time after the end of each neutron burst (referred to as the counting rate xe2x80x9ctime spectrumxe2x80x9d or xe2x80x9cdecay spectrumxe2x80x9d). Prior art processing methods included the assumption that the thermal neutron capture cross-section of the regions within the wellbore are significantly higher than the capture cross-section of the surrounding earth formations. Limitations to these methods are described, for example, in U.S. Pat. No. 4,409,481 issued to Smith et al.
The processing method described in the Smith et al patent includes the assumption that the decay of the gamma ray counting rate with respect to time includes the effects of two and only two distinct exponential decay rates, the first caused by the materials within the wellbore and the second caused by the materials in the earth formations proximal to the wellbore. The method described in the Smith et al patent includes the assumption that the length scales of the materials in the wellbore and in the earth formation are such that the effects of neutron diffusion averages out the actual variations in capture cross-section between the various regions and therefore can be represented by some average value of thermal neutron capture cross-section. As discussed previously, several common conditions exist where this is clearly not the case. Using the processing method described in the Smith et al patent can lead to erroneous results under these conditions.
U.S. Pat. No. 5,973,321 to Schmidt describes a model based method for inversion of thermal neutron decay data. The method includes generating a data kernel which is made up of representors, or models, of potential decay components of the wellbore and of the earth formations in the vicinity of the wellbore. A thermal neutron decay spectrum is measured by a pulsed neutron instrument including a controllable source of high energy neutrons and one or more gamma ray detectors at spaced apart locations from the source. The decay spectrum measured by the instrument is inverted to determine model parameters by which the individual representors are scaled so that when combined, the scaled representors most closely match the measured decay spectrum. A potential disadvantage of model based inversion methods such as that taught by Schmidt is that the curve fitting may give different results depending upon the choice of the model used to generate the data kernel.
There is a need for a method of determination of the components of thermal neutron decay that does not use any predetermined models. The present invention satisfies this need.
The present invention is a method for obtaining parameters of interest of subterranean earth formations using measurements that comprise two or more exponentially decaying functions of time, such as those made using a pulsed neutron logging tool. A fit is made using a single exponential to the tail end of the data and the beginning of the fitting window is selected so that a product of the goodness of fit and the standard error of the fit attains a minimum. The process may be used for determination of thermal neutron capture cross section. By subtracting the determined fit from the measurements, the process may be repeated to find additional components of the decay spectrum.